dextercioby said:In classical field theory one can show that the Hamiltonian, when calculated on the hypersurface of the solutions of the Hamilton's field equations, is equal to the "00" component of the en-mom tensor calculated on the stationary surface of Lagrange's field equations.
As for them being matrices, i guess you mean a quantum theory context in which the hamiltonian is the more important object of the two, since it governs the S-matrix.
A Hamiltonian is a mathematical function that describes the total energy of a system in classical mechanics. It is related to energy and momentum through the Hamiltonian equations, which describe how the energy and momentum of a system change over time.
In quantum mechanics, the Hamiltonian is used to calculate the energy levels and dynamics of a system. It plays a crucial role in determining the behavior of quantum systems and is used to solve the Schrödinger equation, which describes the evolution of a quantum system over time.
In general relativity, the energy momentum tensor is a mathematical object that describes the distribution of matter and energy in space-time. It is used to calculate the curvature of space-time and determine the gravitational field equations.
Yes, the Hamiltonian and energy momentum tensor can be applied to all physical systems, from classical mechanics to quantum mechanics to general relativity. They are fundamental concepts in physics and are used to understand the behavior of various physical systems.
The Hamiltonian is related to the conservation of energy in a system, while the energy momentum tensor is related to the conservation of momentum. In other words, the Hamiltonian describes the total energy of a system, while the energy momentum tensor describes how energy and momentum are conserved within the system.